Relative Prices, Real Wages, and Macroeconomic Policies: Some Evidence from Manufacturing in Japan and the United Kingdom

Leslie Lipschitz; Susan M Schadler

doi:10.5089/9781451946918.024.A002

Author:

Mr. Leslie Lipschitz

Mr. Leslie Lipschitz
Search for other papers by Mr. Leslie Lipschitz in
Current site
Google Scholar

and

Ms. Susan M Schadler

Ms. Susan M Schadler
Search for other papers by Ms. Susan M Schadler in
Current site
Google Scholar

Publication Date:: 01 Jan 1984

eISBN:: 9781451946918

Language:: English

Keywords:: SP; wage gap; output price; input price disturbance; oil price increase; cost share; Wages; Employment; Wage gap; Wage adjustments

Download PDF (1.8 MB)

As inflation appears to have been brought under control in many industrial countries, the discussion about both the timing and the degree of reflationary policies is attracting greater attention. The debate centers on the extent to which consolidation of the gains against inflation should be given priority over demand stimulus to increase growth and employment. Too often, however, insufficient attention is given to the fact that, even among countries that have relatively low inflation rates, there are important differences in underlying conditions that should influence the stance of policy. This paper attempts to point out and to quantify some of these differences.

Abstract

Industries in most countries were buffeted by similar relative price changes—principally large and sudden increases in the costs of raw materials and fuels—during the 1970s, but countries differed in their adjustment to these changes. It is easy to characterize the polar extremes of the adjustment continuum: at one extreme, real wages (or the growth of real wages) remained unchanged, thereby pushing onto profits the entire burden of adjustment to the input price shocks; at the other extreme, real wages were cut sharply to maintain profit shares. The position of countries on the adjustment continuum between these polar extremes has been critical to the debate as to the nature and origin of the recent recession. For countries close to the first extreme, it is arguable that the problem resides essentially in low profitability and high unit labor costs, owing to the unwillingness of labor to accept some of the burden of adjustment to higher input prices during the 1970s. According to this view, recent poor output and employment performance is due more to relative price developments than to inadequate domestic demand and is therefore less amenable to correction by demand management policies. Indeed, without a period of tight demand management and some slack in employment, it might not have been possible to dampen inflationary expectations and restore a sense of realism to the labor market. For countries that have managed a greater degree of wage adjustment, it can be argued that the recession has persisted largely because of a dearth of demand. In this case, less stringent demand management might now facilitate more rapid growth and an environment more conducive to an improvement in economic fundamentals.

This paper draws on and updates work done within the Fund during the past few years in an attempt to quantify aspects of this discussion.¹ The quantification concentrates on a comparison of the manufacturing sectors in Japan and the United Kingdom during the period 1962–82. Although both countries were seriously affected by the input price disturbances of the 1970s, it is generally believed that they were quite different in their adjustment to these disturbances. Wage developments have been the focus of attention in both countries. In Japan the labor market can generally be characterized as flexible, with a relatively unified system for annual wage negotiations and a strong social consensus allowing for a sharing between capital and labor of the burden of adjustment. In the United Kingdom the labor market is usually seen as having been less flexible, with wage settlements based on short-term power relationships between government, management, and unions rather than on agreement about employment and sustainable wage increases over the longer run. Thus, while real wage increases in Japan accelerated from the late 1960s through the middle of the 1970s, this acceleration gave rise to relatively little political tension and contributed to the emergence of a consensus on the need for more moderate wage behavior. In the United Kingdom, in contrast, wage disputes and developments contributed to the fall of the government in 1974 and have been at the center of political debate during the past decade. Formal incomes policies, which seemed to meet with some short-term successes in 1976–78, were subsequently abandoned. Because of these differences between the conventional perceptions of Japan and the United Kingdom, these two countries seem likely candidates for fruitful comparison.

The plan of the paper is as follows. In Section I the questions to be addressed are specified, and the simple model for their analysis is described and estimated. In Section II the results of the econometric work are used to analyze wage developments. Finally, in Section III, inferences are drawn from the analysis for the conduct of macroeconomic policies.

I. Relative Prices and Cyclical Influences in the Manufacturing Sector

two views

In both Japan and the United Kingdom, the performance of the manufacturing sector has deteriorated since the mid-1970s in terms of output, employment, profitability, and productivity (Chart 1 and Tables 1 and 2). The model described in this section attempts to separate various influences on output and employment in manufacturing.

Chart 1.

Japan and the United Kingdom: Performance in the Manufacturing Sector, 1963–82

(Annual percentage change)

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.¹ Productivity is normalized to eliminate the cyclical component.² Employment is measured in terms of man-hours worked.

Table 1.

Japan: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

^²1973–81.

^³Yield on longest remaining maturities of interest-bearing Nippon Telephone and Telegraph bonds, deflated by the actual increase in consumer prices during this period.

^⁴Includes cash earnings of workers plus employment taxes paid by employers.

Table 1.

Japan: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Item		1963–72	1973–82
Manufacturing output		11.6	3.2
Labor input (hours worked)		1.6	−0.3
Productivity in manufacturing
	(normalized)¹	11.0	5.9
Gross real fixed investment
	in manufacturing	12.7	5.5
Share of capital in value added
	(in percent, average rate)	54.3	44.7²
Real rate of interest (average rate)³		2.7	—
Output price index (all manufactured
	products)	1.0	6.7
Hourly compensation in manufacturing⁴		13.5	10.7
Input price index (materials and fuels
	purchased by manufacturing industry)	1.9	13.6

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

^²1973–81.

^³Yield on longest remaining maturities of interest-bearing Nippon Telephone and Telegraph bonds, deflated by the actual increase in consumer prices during this period.

^⁴Includes cash earnings of workers plus employment taxes paid by employers.

Table 1.

Japan: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Item		1963–72	1973–82
Manufacturing output		11.6	3.2
Labor input (hours worked)		1.6	−0.3
Productivity in manufacturing
	(normalized)¹	11.0	5.9
Gross real fixed investment
	in manufacturing	12.7	5.5
Share of capital in value added
	(in percent, average rate)	54.3	44.7²
Real rate of interest (average rate)³		2.7	—
Output price index (all manufactured
	products)	1.0	6.7
Hourly compensation in manufacturing⁴		13.5	10.7
Input price index (materials and fuels
	purchased by manufacturing industry)	1.9	13.6

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

^²1973–81.

^³Yield on longest remaining maturities of interest-bearing Nippon Telephone and Telegraph bonds, deflated by the actual increase in consumer prices during this period.

^⁴Includes cash earnings of workers plus employment taxes paid by employers.

Table 2.

United Kingdom: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

Table 2.

United Kingdom: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Item		1963–72	1973–82
Manufacturing output		3.0	−1.2
Labor input (hours worked)		−1.5	−3.9
Productivity in manufacturing
	(normalized)¹	4.5	2.3
Gross real fixed investment
	in manufacturing	0.9	−2.3
Pretax real rate of return on capital
	(average rate)	10.1	5.7
Cost of capital (average rate)		5.1	6.3
Output price index (all manufactured
	products)	4.0	13.5
Hourly earnings in manufacturing		8.7	16.5
Input price index (materials and fuels
	purchased by manufacturing industry)	3.6	17.0

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

Table 2.

United Kingdom: Some Basic Data on Manufacturing, 1963–82

(Average annual percentage change unless otherwise specified)

Item		1963–72	1973–82
Manufacturing output		3.0	−1.2
Labor input (hours worked)		−1.5	−3.9
Productivity in manufacturing
	(normalized)¹	4.5	2.3
Gross real fixed investment
	in manufacturing	0.9	−2.3
Pretax real rate of return on capital
	(average rate)	10.1	5.7
Cost of capital (average rate)		5.1	6.3
Output price index (all manufactured
	products)	4.0	13.5
Hourly earnings in manufacturing		8.7	16.5
Input price index (materials and fuels
	purchased by manufacturing industry)	3.6	17.0

Sources: Data sources are listed in Appendix I.

^¹Based on value added and normalized to exclude cyclical fluctuations.

In classical terms, profit-maximizing producers of manufactured goods are assumed to choose the amounts of output they supply and inputs they use by employing all variable factors of production up to the point where the marginal product of each is equal to its product price. Output prices, in turn, adjust to ensure that any level of output is absorbed by consumers. This proposition leads to the conclusion that the increases in real wages or real prices of raw materials during the past decade have reduced the profit-maximizing levels of both labor and material inputs and of production.²

The Keynesian counterargument holds that, while relative price shifts have had a depressing effect on employment and output, a deficiency of demand has far overshadowed this influence. In other words, at the given historical relative price levels, producers have been forced to produce less than they would have produced if they had not been constrained by demand. Output, rather than prices, adjusted downward—that is, producers have been off their supply curves, and demand, rather than supply, has been the operative constraint. The issue addressed in this section is the following: To what extent has the decline in the growth of output and employment in manufacturing been due (1) to higher real wages and prices of raw materials and (2) to a deficiency of demand?

The two arguments are depicted in Figure 1. SS is the locus of points at which real wages are such that firms are willing to supply the amount of output demanded. It embodies a given state of technology and stock of capital and is negatively sloped to indicate that an increase in employment (and therefore supply) requires a reduction in real wages. The vertical line drawn at y* represents full employment. The area to the left of SS represents Keynesian unemployment. The area to the left of the full employment line (Y*), but on or to the right of SS, represents classical (high-wage) unemployment.

Figure 1.

Keynesian and Classical Unemployment

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Source: Basevi and others (1983, p. 8); adapted from the early disequilibrium model of Mundell (1964).

At point C, for example, output is constrained by demand, which amounts to 0D, while at the given real wage rate W₀ firms would willingly produce 0E. Clearly, demand stimulus could increase output to point B. At this point, however, real wages become the operative constraint. Supply would be impervious to further demand expansion unless real wages were reduced.³ At any real wage above W*, there will not be full employment. Unemployment may be purely classical, as at point B, or a combination of classical and Keynesian, as at point C. The analysis that follows attempts to separate these influences.

the model

It is easiest to begin with a simple framework relating gross manufactured output to three factors of production: labor, capital, and raw materials. Upon substitution of the condition that marginal products equal real prices for each variable input,⁴ a production function may be derived that relates output to product wages, product prices of raw materials, technological change, and the capital stock. Similarly, a labor demand equation can be derived from the condition that the marginal product of labor equals the real wage. To the strictly classical framework of these equations is added an expression to reflect cyclical changes in demand that temporarily push producers off their desired supply functions:⁵

\begin{matrix} q & = c_{1} - (α σ_{1} / γ) (w_{p} - λ_{t} t + λ_{t} t^{2}) \\ - [{β (σ_{1} α + σ_{2} γ)} / {(1 - β) γ}] pr m_{p} + k \\ + m_{1} cyc (- 1) & (1) \end{matrix}

\begin{matrix} n & = c_{2} - [(1 - β) σ_{1} / γ] (w_{p} - λ_{1} t + λ_{2} t^{2}) - (β σ_{1} / γ) pr m_{p} \\ + k - λ_{1} t + λ_{2} t^{2} + m_{2} cyc (- 1) & (2) \end{matrix}

where

Q = gross output in manufacturing
W_p = nominal wages deflated by the price of manufactured output
t = time trend
PRM_p = nominal price of raw material and fuel inputs into manufacturing, deflated by the price of manufactured output
K = capital stock in terms of constant prices
N = total hours worked in manufacturing
CYC = deviations of actual expenditure from a quadratic trend⁶
α, β, γ = shares of labor, raw materials, and capital in total costs.⁷

Lowercase letters of variables (other than t) represent natural logarithms. Changes in the productivity of labor owing to technological progress are proxied by a second-order polynomial in t with parameters λ₁ and λ₁ on t and t², respectively.⁸

Tables 3 and 4 show the results of the estimation of equations (1) and (2), using data from Japan and the United Kingdom (see Appendix I for data sources). For each country, the two-equation system is estimated simultaneously, with across-equation restrictions on parameters imposed to ensure consistency. For both countries, all the estimated structural parameters have the expected signs, are of plausible magnitude, and have very small asymptotic standard errors.

Table 3.

Japan and the United Kingdom: Estimation Results from Manufacturing Output and Labor Demand Equations¹

^¹The model was estimated, using annual data for 1962 through 1982, by a three-stage least-squares program that allows for across-equation constraints on parameters. Numbers in parentheses are asymptotic standard errors on the corresponding parameter estimates.

^²Differences in the constant terms reflect differences in the index bases rather than differences that are economically meaningful.

^³Cost share of raw materials in total inputs. The shares of labor and capital were obtained from national income statistics and were not estimated.

^⁴Elasticity of substitution between labor and capital.

^⁵Elasticity of substitution between value added and raw materials.

^⁶The estimate of λ₂ for the United Kingdom was significantly different from zero at the 99 percent level of confidence. The standard error was negligible in the three-decimal-place format of the table.

Table 3.

Japan and the United Kingdom: Estimation Results from Manufacturing Output and Labor Demand Equations¹

Structural Parameter	Japan		United Kingdom²
c ₁ ²	−0.474	(0.042)	6.632	(0.515)
c ₂ ²	0.186	(0.042)	9.322	(0.602)
β³	0.277	(0.018)	0.165	(0.046)
σ₁⁴	0.409	(0.014)	0.518	(0.056)
σ₂⁵	0.586	(0.168)	0.540	(0.268)
λ ₁	0.056	(0.005)	0.057	(0.004)
λ ₁ ⁶	—		0.001	(0.000)
m ₁	1.578	(0.278)	1.016	(0.432)
m ₂	0.314	(0.126)	1.271	(0.542)
Standard error of estimate	0.048		0.045
Pearsonian squared correlation coefficient	0.99		0.95

^²Differences in the constant terms reflect differences in the index bases rather than differences that are economically meaningful.

^³Cost share of raw materials in total inputs. The shares of labor and capital were obtained from national income statistics and were not estimated.

^⁴Elasticity of substitution between labor and capital.

^⁵Elasticity of substitution between value added and raw materials.

Table 3.

Japan and the United Kingdom: Estimation Results from Manufacturing Output and Labor Demand Equations¹

Structural Parameter	Japan		United Kingdom²
c ₁ ²	−0.474	(0.042)	6.632	(0.515)
c ₂ ²	0.186	(0.042)	9.322	(0.602)
β³	0.277	(0.018)	0.165	(0.046)
σ₁⁴	0.409	(0.014)	0.518	(0.056)
σ₂⁵	0.586	(0.168)	0.540	(0.268)
λ ₁	0.056	(0.005)	0.057	(0.004)
λ ₁ ⁶	—		0.001	(0.000)
m ₁	1.578	(0.278)	1.016	(0.432)
m ₂	0.314	(0.126)	1.271	(0.542)
Standard error of estimate	0.048		0.045
Pearsonian squared correlation coefficient	0.99		0.95

^²Differences in the constant terms reflect differences in the index bases rather than differences that are economically meaningful.

^³Cost share of raw materials in total inputs. The shares of labor and capital were obtained from national income statistics and were not estimated.

^⁴Elasticity of substitution between labor and capital.

^⁵Elasticity of substitution between value added and raw materials.

Table 4.

Japan and the United Kingdom: Estimated Equations with Composite Coefficients¹

^¹The models were estimated, using data for 1962–82, by a three-stage least-squares program that allows for across-equation constraints on parameters. Where available, asymptotic standard errors are given in parentheses below parameter estimates.

^²This variable was contemporaneous in the estimates for Japan but lagged one period in the estimates for the United Kingdom.

Table 4.

Japan and the United Kingdom: Estimated Equations with Composite Coefficients¹

		Composite Coefficient Estimates
Country		Constant	w_p	prm_p ²	t	t ²	cyc(−1)
Japan
	1. Output per unit of capital (q − k)	−0.474 (0.417)	−0.419	−0.386	0.024	—	1.578 (0.278)
	2. Labor demand per unit of capital (n − k)	0.186 (0.042)	−0.829	−0.318	−0.010	—	0.314 (0.126)
United Kingdom
	1. Output per unit of capital (q − k)	6.632 (0.515)	−1.279	−0.359	0.073	−0.001	1.016 (0.432)
	2. Labor demand per unit of capital (n − k)	9.322 (0.602)	−1.797	−0.354	0.046	−0.001	1.271 (0.542)

^²This variable was contemporaneous in the estimates for Japan but lagged one period in the estimates for the United Kingdom.

Table 4.

Japan and the United Kingdom: Estimated Equations with Composite Coefficients¹

		Composite Coefficient Estimates
Country		Constant	w_p	prm_p ²	t	t ²	cyc(−1)
Japan
	1. Output per unit of capital (q − k)	−0.474 (0.417)	−0.419	−0.386	0.024	—	1.578 (0.278)
	2. Labor demand per unit of capital (n − k)	0.186 (0.042)	−0.829	−0.318	−0.010	—	0.314 (0.126)
United Kingdom
	1. Output per unit of capital (q − k)	6.632 (0.515)	−1.279	−0.359	0.073	−0.001	1.016 (0.432)
	2. Labor demand per unit of capital (n − k)	9.322 (0.602)	−1.797	−0.354	0.046	−0.001	1.271 (0.542)

^²This variable was contemporaneous in the estimates for Japan but lagged one period in the estimates for the United Kingdom.

In Japan the average share of raw material costs in gross output is estimated at 28 percent. The implied shares of labor and capital in gross output are about 37 and 36 percent, respectively. Labor productivity growth is estimated to be about 5.6 percent, on average, over the period. The elasticity of substitution between raw materials and value added—that is, capital plus labor—is estimated to be 0.586. This figure is important because it indicates the degree to which capital and labor can be substituted for raw materials as their relative prices change.⁹ The elasticity of substitution between capital and labor is estimated to be 0.409. These results imply that increases in the real price of raw materials and in real wages over the period were only partially offset by reductions in the use of these inputs. Consequently, their shares in total costs increased at the expense of profits. Finally, the coefficients on the cyclical variable (1.58 for output and 0.31 for labor demand) indicate that a 1 percent increase in actual demand relative to trend gives rise to an almost 1.6 percent increase in manufactured output and an increase of just under ⅓ of 1 percent in labor demand.

In the United Kingdom, the average share of raw material costs in gross output was 16.5 percent. While this initially seemed rather low, it corresponded very closely to the coefficient obtained from the 1974 input-output tables.¹⁰ The implied average shares of labor and capital were 59.5 percent and 24 percent, respectively.¹¹ Labor productivity growth, characterized by a quadratic in time, shows a dramatic slowing down in the latter part of the period, owing to the small but highly significant coefficient on t². Along this curve, productivity growth falls from about 5.6 percent at the beginning of the sample period to about 1.6 percent at the end of the period. Point estimates of both the elasticity of substitution between capital and labor and that between raw materials and value added are about 0.5. The asymptotic standard errors indicate greater confidence that the first elasticity is significantly smaller than unity than that the second is. This result suggests that we may be fairly confident that higher wages reduce the share of capital, but less confident that higher raw material prices reduce the combined share of labor and capital. The coefficient on the cyclical variable shows that manufacturing output has cycles of greater amplitude than aggregate expenditure. The cyclical coefficient in the labor demand equation is surprisingly large. It is probably larger than that in most other estimates for two reasons: the importance of the most recent cycle (in which there was little trace of labor hoarding) in the sample; and the use of a quadratic in time, rather than a simple trend, to derive the cyclical variable. The difference between Japan and the United Kingdom in labor hoarding during cyclical downturns is brought into sharp relief by the estimated values of m₂; a 10 percent fall below trend in Japanese aggregate demand reduces man-hours worked in manufacturing by only 3.1 percent, whereas a similar downturn in the United Kingdom reduces man-hours in manufacturing by 12.7 percent.

On the basis of the estimated equations, it is possible to separate the contributions of the various explanatory variables to output and labor demand. Table 5 does this separately for the first decade (1963–72) and the second decade (1973–82) of the sample period. The results are not very dramatic because they are averaged over ten-year periods (clearly, if one were to look at single years immediately after oil price shocks or major union wage offensives, the results would be more dramatic), but they are in line with expectations. The fall in output growth in the second decade is striking in the United Kingdom, but even sharper in Japan. In both countries the lower rate of capital accumulation is the major explanatory factor behind the fall in growth, but, as expected, higher material prices contribute significantly to this fall, as does the dearth of aggregate demand. Of interest is that real wage costs contribute negatively to output in Japan in the first decade, but positively in the second; in the United Kingdom, the negative wage-push effects worsen from the first to the second decade. The labor demand equations exhibit similar causal influences, showing a sharp negative effect from wages in the first decade in Japan that is turned around in the second, and a worsening of the real wage position in the United Kingdom.

Table 5.

Japan and the United Kingdom: Components of Change in Output and Labor Demand, 1963–82

(Annual percentage change)

^¹Adjusted for changes in productivity.

Table 5.

Japan and the United Kingdom: Components of Change in Output and Labor Demand, 1963–82

(Annual percentage change)

			1963–72		1973–82
Item			Japan	United Kingdom	Japan	United Kingdom
Output			11.561	3.037	3.222	−1.235
	Wages¹		−2.855	−0.987	0.680	−1.620
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.346	0.194	−2.653	−1.288
	Cyclical influence		1.404	0.084	−1.069	−0.386
	Unexplained residual		0.473	−0.429	−0.071	0.045
Labor demand			1.611	−1.540	−0.288	−3.910
	Wages¹		−5.640	−1.387	1.344	−2.276
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.285	0.192	2.187	−1.272
	Cyclical influence		0.279	0.105	−0.213	−0.483
	Labor-saving
		technology	−5.635	−3.943	−5.635	−1.708
	Unexplained residual		−0.007	−0.682	−0.358	−0.185

^¹Adjusted for changes in productivity.

Table 5.

Japan and the United Kingdom: Components of Change in Output and Labor Demand, 1963–82

(Annual percentage change)

			1963–72		1973–82
Item			Japan	United Kingdom	Japan	United Kingdom
Output			11.561	3.037	3.222	−1.235
	Wages¹		−2.855	−0.987	0.680	−1.620
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.346	0.194	−2.653	−1.288
	Cyclical influence		1.404	0.084	−1.069	−0.386
	Unexplained residual		0.473	−0.429	−0.071	0.045
Labor demand			1.611	−1.540	−0.288	−3.910
	Wages¹		−5.640	−1.387	1.344	−2.276
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.285	0.192	2.187	−1.272
	Cyclical influence		0.279	0.105	−0.213	−0.483
	Labor-saving
		technology	−5.635	−3.943	−5.635	−1.708
	Unexplained residual		−0.007	−0.682	−0.358	−0.185

^¹Adjusted for changes in productivity.

II. Wage Push, Factor Shares, and Employment

In comparing actual wage movements with those warranted by underlying conditions, the conventional model focuses on cost shares of factors of production and defines warranted wage movements as those that are consistent with constant cost shares in value added. This is a reasonable approach if one is concerned with the incidence of the burden of an increase in raw material prices—cost shares in value added that are fixed would mean an equal sharing of the burden. Over time, however, there are likely to be other influences on warranted wage movements. For example, in a situation with relatively abundant capital but a binding labor supply constraint, the market-clearing wage rate might well be above that which maintains fixed cost shares. To calculate the warranted wage in this situation, a labor supply function must be added to the labor demand equation estimated in the previous section. In addition, the elasticity of substitution between capital and labor becomes relevant to the determination of the warranted wage rate.

The sections that follow begin with the conventional analysis, then introduce considerations of the labor supply, and conclude with a recalculation of warranted wage movements that are consistent with the estimated equations and a given supply of labor. While the policy implications for the 1980s are not much affected by differences between the conventional analysis and the more elaborate calculations, the latter do help to resolve some puzzles raised by the conventional analysis.

actual and warranted wage increases: the conventional analysis

In the production functions from which the estimated equations were derived, the degree of homogeneity was set at unity to ensure that the total product would be exactly exhausted if factors were paid their marginal products. On the basis of estimated factor shares, it is therefore possible to disaggregate the unit output price of manufactures into wage costs, raw material costs, and the cost of capital per unit of output. In percentage changes (that is, differences of logarithms, represented by dots over variables), therefore

\begin{matrix} \dot{p} = (\dot{w} - p \dot{r} od) + βp \dot{r} m + γ \dot{r} & (3) \end{matrix}

where α (see equation (4)), β, and γ are, respectively, cost shares of labor, materials, and capital in gross output, and where

p = output price
w = nominal wage rate
prod = labor productivity
prm = nominal price of raw materials
r = nominal cost of capital.

Expressing all prices in terms of output prices and rearranging equation (3), the relationship between the real cost of capital per unit of output and the relative price changes is

\begin{matrix} {\dot{r}}_{p} = - (α / γ) ({\dot{w}}_{p} - p \dot{r} od) - (β / γ) p \dot{r} m_{p} & (4) \end{matrix}

where p subscripts denote nominal prices relative to output prices. Clearly, increases in real wages in excess of productivity growth and increases in real prices of raw materials reduce the share of output going to capital. Since changes in this share translate into changes in the rate of return on capital when changes in the capital stock are small, r_p directly affects investment incentives.

Equation (4) is particularly useful in highlighting the fundamental relationship between wage behavior and the shares of capital in output and, therefore, in formulating an objective for wage determination, given developments in productivity and raw material prices. In the extreme, for example, one could set as an objective that wages adjust to maintain a constant real flow to capital per unit of output (that is, ${\dot{r}}_{p} = 0$ ). This would require that wages bear the entire burden of terms-of-trade changes and adjust according to the following formula:

{\dot{w}}_{p} = p \dot{r} od - (β / α) p \dot{r} m_{p} .

For Japan, given the estimated factor shares, product wages would have to decline by approximately three quarters of a percentage point for every point of increase in the relative price of raw materials; for the United Kingdom, the coefficient is lower at slightly over a quarter. During the second decade of the sample period, this would have required an increase in real product wages of only 18 percent in Japan and 13 percent in the United Kingdom, compared with the actual increases of 40 percent and 30 percent, respectively.

An alternative, and probably more reasonable, objective for wage adjustments, given the large changes in raw materials prices in recent years, is the maintenance of the shares of labor and capital in value added, which implies an equal sharing by capital and labor of any terms-of-trade loss resulting from increases in prices of materials. Wage changes following this objective, which are called here “warranted” changes in real wages (ww_p), can be characterized as follows:

\begin{matrix} w {\dot{w}}_{p} = p \dot{r} od - (β / (1 - β)) p \dot{r} m_{p} . & (5) \end{matrix}

In calculating warranted real wage changes according to equation (5), the price of labor relative to capital is held constant by construction so that, even if the elasticity of substitution between capital and labor differs from unity, the shares of these factors in value added will not change. No such construction, however, is applicable to the share of raw materials (β) in gross output; therefore, insofar as the elasticity of substitution is less than unity, the share of raw materials will vary positively with the relative price of raw materials. For this reason, in calculating warranted real wage changes, it is necessary to adjust the estimated average value of β for relative price changes, using the estimated elasticity of substitution (see Appendix II for the precise adjustment required).

Before proceeding to compare actual and warranted real wage movements in Japan and in the United Kingdom, it is useful to compare the starting points, in 1961, when the share of labor in value added in Japan was 44 percent and that in the United Kingdom was 69 percent. At the beginning of the sample period the portion of value added appropriated by labor in the United Kingdom was so large that a substantial and sustained larger wage gap (that is, actual less warranted real wage increases) in Japan would be required before factor shares could be equalized.

The top panel of Chart 2 shows actual and warranted changes in real wage rates in Japan; the bottom panel shows the corresponding real wage levels. In Chart 3 the same information is provided for the United Kingdom. The data are quite dramatic and, superficially at least, seem to undermine the conventional perceptions of the two countries. In Japan actual wages rose more rapidly than warranted by the calculations in this study, beginning in the second half of the 1960s—thereby opening up a sizable wage gap. By the beginning of the second decade of the sample period (1973), the actual real wage level in Japan was already some 20 percent higher than the warranted level, while in the United Kingdom there was still no significant difference. Subsequently, in both countries the input price disturbances and the slowdown in productivity growth sharply reduced warranted rates of change of real wages.

Chart 2.

Japan: Actual and Warranted Real Wage Developments, 1962–82

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.

Chart 3.

United Kingdom: Actual and Warranted Real Wage Developments, 1962–82

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.

It is interesting to compare the wage performance of Japan and the United Kingdom in each of the two decades of the sample period. To facilitate this comparison, wage gap indices were computed separately for 1963–72 and 1973–82.¹² The top panel of Chart 4 shows wage gap indices for the two countries (1967 = 100) during 1963–72. In this decade—one of rapid (11½ percent annual average) expansion of output in Japan and modest (3 percent annual average) expansion of output in the United Kingdom—the indices show a substantial wage gap emerging in Japan but virtually none emerging in the United Kingdom. Notably, the dip in the wage gap in 1967–68 in the United Kingdom coincided with the devaluation of sterling in November 1967. This suggests that the devaluation was sustained, at least for a couple of years, in real terms. Despite the much larger wage gap indicated for Japan, by the end of this decade the share of labor in value added in Japanese manufacturing had risen to only 48 percent, compared with 69 percent in the United Kingdom.

Chart 4.

Japan and the United Kingdom: Wage Gap Indices,¹ 1963–82

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.¹ The wage gap is measured simply as an index of the actual over the warranted real wage level.

The bottom panel of Chart 4 shows wage gap indices for 1973–82 (1977 = 100). In this decade, which was characterized by a deterioration of output performance and an erosion of the share of profits in value added in both countries, the wage gap worsened in the United Kingdom more than in Japan. In Japan, actual real wages rose much more rapidly than the warranted rates during the two years following the 1973 oil price increase. After 1975, however, the wage gap index saw no further increase for the rest of the sample period. In the United Kingdom, too, real wages rose rapidly during 1974 and 1975 despite the reductions in the warranted rate of increase. Wage settlements in 1973–74 were influenced by the Stage III incomes policy, which encouraged cost of living adjustments in private wage agreements. A sharp downward adjustment, or correction, was achieved during 1976–77, with real wages falling by more than 6 percent over the two-year period, but subsequently the position deteriorated rapidly.

Developments during the most recent period—say, 1975–82, giving the economies a year to adjust after the first oil shock—provide a useful perspective on the problems that policymakers in these countries now face. By historical standards, manufacturing output and employment have been depressed in both countries, but, while in Japan the annual average growth rates of these variables simply slowed, in the United Kingdom output and employment actually fell. In Japan the first wave of increases in prices of materials in 1973–74 lowered the share of capital in value added, but shares stabilized after 1975, and there was no significant further erosion of the share of capital. Both the sharp decline in the growth of the capital stock in manufacturing and, to a lesser extent, the cyclical position of the economy, however, had a negative influence on both output and employment. In the United Kingdom the wage gap widened significantly after the 1976–77 adjustment. At the same time, changes in the cyclical position and a slowdown in the growth of the capital stock were important factors behind the decline in output and employment.

the supply of labor and the real wage

In examining the data thus far, it has been difficult to draw valid inferences because of the partial equilibrium nature of the analysis. The implicit assumptions behind this sort of wage gap measurement are that the price of labor is set exogenously and that employment is determined by demand. In modeling only the manufacturing sector, it is difficult to take proper account of changes in the supply of labor. A shift of the labor demand function in some other sector would affect the supply to manufacturing quite independently of developments in manufacturing itself. Nevertheless, to appreciate the differences between Japan and the United Kingdom, it is useful to depart for a moment from the formal, exogenous wage model and to consider simultaneously the demand for and supply of labor.

As has been noted, the substantial (14 percent annual average) rise in real wages in Japan between 1966 and 1972 was much greater than the (11 percent annual average) rate required to maintain factor shares in value added. It is not clear, however, whether this sharp increase in the share of labor in value added was due to wage push or was an equilibrating response to a labor supply constraint. To answer this question, it is useful to look at what would have happened to output growth and the demand for labor if actual wage rates had moved like warranted wage rates—; that is, if wages had moved simply to maintain factor shares in value added.

Between 1966 and 1972, actual output in manufacturing in Japan rose at an annual average rate of 12 percent, and employment rose at an annual average rate of 1.3 percent. If wages had moved simply to maintain distributional shares, output would have risen at an average rate of almost 15 percent, and labor demand at an average rate of 4.5 percent a year. Even with the rapid actual real wage increases, the total labor force rose by only 1.1 percent a year, so that an annual increase of 4.5 percent in employment in manufacturing would have been quite impossible, especially given the growth of the services sector (Chart 5). It would be difficult not to conclude from this exercise that, at least before 1973, actual wage increases in Japan were largely a market-equilibrating phenomenon. Wage increases, if not warranted in the sense of maintaining factor shares, were certainly warranted in the sense of reconciling the demand for labor with the scarce supply. In contrast, the large increase in actual wages (and the share of labor costs in output) between 1973 and 1975 coincided with a sharp drop in the demand for labor; this suggests that wage movements were not simply a market-clearing mechanism in these two years.

Chart 5.

Japan and the United Kingdom: Labor Demand in Manufacturing and Total Labor Force Growth,¹ 1963–82

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.¹ Labor demand in manufacturing is measured in hours worked. Labor demand at warranted wage is obtained by simulating labor demand with wage rates set equal to warranted wage rates. The actual labor demand in manufacturing and the total work force are measured as indices, with the value in 1980 set equal to 100. The simulated labor demand at warranted wage is derived from the estimate of equation (2).

In the United Kingdom the view that employment is demand determined, that the supply of labor is not an important constraint on employment in manufacturing, and that wage rates are not determined so as to clear the labor market is more plausible. In 1963–72, when actual wage movements were close to warranted wage movements, employment (that is, man-hours) in manufacturing fell, on average, by 1½ percent a year; in 1973–82, despite an average annual reduction in employment of more than 3½ percent, actual real wage increases exceeded warranted increases, on average, by 1½ percentage points a year. Obviously, the classical wage-employment mechanics are being obscured to some extent by structural change as the share of the manufacturing sector in the economy shrinks. But it is clear from unemployment developments in the most recent period that the fall in manufacturing employment is not a matter of workers being bid away by other sectors as the economic structure adjusts. Rather, the fall in manufacturing employment and the wage push have coincided with growing unemployment.

an alternative warranted wage calculation

An alternative approach to the wage gap analysis that takes account of the supply of labor relative to that of capital and the elasticity of substitution between them may be derived by inverting equation (2) and setting labor demand equal to labor supply. The following equation for the warranted change in the real wage rate emerges:

\begin{matrix} w {\dot{w}}_{p} & = λ_{1} [1 - γ / σ_{1} (1 - β)] - λ_{2} [1 - γ / σ_{1} (1 - β)] (t^{2} - t {(- 1)}^{2}) \\ - (β (1 - β)) p \dot{r} m_{p} + (γ / σ_{1} (1 - β)) (\dot{k} - \dot{n}) \\ + m_{2} (γ / σ_{1} (1 - β)) c \dot{y} c (- 1) . & (6) \end{matrix}

To determine warranted wage movements from this equation, it is assumed that the supply of labor to manufacturing grows at the same rate as the total work force. This is not an entirely satisfactory assumption, but it is neutral. Alternatively, one could build into the labor supply estimates some concept of structural change that reduces the supply of labor to manufacturing in favor of that available to other sectors.¹³ This methodology poses two serious difficulties, particularly for the United Kingdom. First, it would apply to the extent that workers were bid away from manufacturing by competition from other sectors, but it would not be appropriate if the decline in employment in manufacturing swelled the ranks of the unemployed. Second, it is very difficult to separate an independent process of structural change from one induced by high wages and low profits in manufacturing. If it can be argued that much of the shrinkage of the manufacturing sector is due to the uneconomically high labor costs that we are trying to measure, then this shrinkage may reflect more the demand for labor (given wage rates) than a reduction in the supply of labor to manufacturing. Nevertheless, even though it may be difficult to measure, some independent structural change certainly has occurred in both Japan and the United Kingdom, so that some error in our estimate of the growth of the supply of labor to manufacturing is inevitable. Because this error cumulated over 20 years is likely to be significant, it would be wrong to draw strong inferences from our estimates of the absolute size of the wage gap that develops over the entire sample period. For this reason, we have presented the wage gaps in index form, with a midpoint in each decade as the index base, and have focused our discussion more on large changes in the wage gaps in particular periods than on absolute levels.

The wage gap indices derived by means of equation (6) are shown in Chart 6, which, for ease of comparison, is set up in the same form as Chart 4. In 1963–72, the wage gap that emerged for Japan in the conventional analysis (and that appeared to be related to a labor supply constraint) is now entirely absent. Indeed, the actual wage relative to the warranted wage falls by about 2 percent over the decade. The difference between the results of this analysis and the conventional analyses is largely due to the explicit introduction of the capital-labor ratio, which rose very rapidly throughout the period until 1973 and produced a large warranted increase in the share of labor. The performance of the United Kingdom over the same period is slightly less satisfactory than it seemed from our initial calculations; the wage gap increases by 6 percent over the period compared with an increase of less than 4 percent in the conventional calculation.

Chart 6.

Japan and the United Kingdom: Alternative Wage Gap Indices,¹ 1963–82

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A002

Sources: Data sources are listed in Appendix I.¹ The wage gap is measured simply as an index of the actual over the warranted real wage level.

During 1973–82 the wage gap that emerges from this analysis is somewhat larger than that in the conventional calculations, but the pattern of changes is similar. In both countries, there is a large increase in the wage gap in the immediate aftermath (one or two years) of the first oil price increase. In the United Kingdom, this is corrected sharply in 1977, with both real wages and the wage gap being reduced by about 7 percent. Subsequently, there is a continuous deterioration in the wage gap in the United Kingdom that is exacerbated by the second oil shock. In Japan, there is no correction of the wage gap that emerged after the first oil shock, but the adjustment to the second oil shock is far better than that in the United Kingdom. While the wage gap in Japan increased by less than 2 percent between 1978 and 1982, it increased by 14½ percent during the same period in the United Kingdom. Purged of cyclical influences, the gap increased by only slightly more than 1 percent in Japan, but by 11 percent in the United Kingdom.

To gain some perspective on considerations relevant to the current stance of macroeconomic policy, it is again useful to examine more closely the period 1975–82. Developments affecting labor’s position in wage negotiations and the evolution of the real economy contributed to the determination of wage gaps during this period. Fluctuations in nominal exchange rates, which frequently translated into changes in the real exchange rate (measured as relative unit labor costs) constituted an additional influence on wage gaps. To the extent that labor costs are sticky in domestic currency terms, and that international competition limits changes in foreign currency prices of output, a real depreciation tends to redistribute income away from labor toward capital. A depreciation therefore enhances international competitiveness and, in the terminology used here, reduces the wage gap relative to that of trading partners.

In Japan the relative stability of the wage gap between 1975 and 1982 is impressive when viewed against developments in the exchange rate and raw material prices during the period. The yen appreciated against the U.S. dollar by 57 percent between early 1976 and late 1978; dollar prices of Japanese products, however, were allowed to increase by about 52 percent, so that export prices in yen declined by only about 5 percent. The needed restraint on wage increases was facilitated by the moderation of consumer price increases as a result of a decline in import prices. Consequently, actual wages moved in line with warranted wages. The response of wages to the second round of oil price increases was contained by two factors. First, the excessive wage growth following the first oil price increase had produced a consensus that sharing the burden of a terms-of-trade loss in order to minimize disruptions to output and employment was beneficial to both employers and employees. (The wage restraint in the first yearly wage negotiation after the 1979 oil price increases resulted in a 7 percent fall in real wages in 1980.) Second, the sharp depreciation of the yen between late 1978 and early 1980 tended to put downward pressure on real wages and to enhance profitability. Consequently, there was a reduction of almost 4 percentage points in the wage gap in 1980. By 1982, the wage gap was still 2 percentage points below the 1979 peak.

In the United Kingdom the period is characterized by quite distinct phases. The first phase saw a remarkable real wage correction in 1976–77, after the widening wage gap of the previous two years. In August 1975 (the beginning of the 1975–76 pay round), an incomes policy was introduced. While this was largely abided by through 1977, it had little apparent effect on the perception of the value of sterling in the foreign exchanges. Thus, while the annual rate of change of average earnings in manufacturing fell from 21½ percent in 1973–75 to less than 13½ percent in 1976–77,¹⁴ the average effective value of sterling in 1976–77 was some 17 percent lower than in 1975.

The second phase saw a rapid deterioration (Buiter and Miller (1981, 1983)). The incomes policy began to disintegrate and was abandoned by the new government in 1979, and the coincidence of a host of developments conspired to exacerbate the situation. First, the emergence of the United Kingdom as a major oil producer, together with the rise in the price of oil, strengthened the external payments position and increased the value of sterling on the exchanges. Second, the announcement and implementation of a strongly anti-inflationary strategy in 1979–80 had inconsistent effects in different markets. The strategy was immediately credible in financial markets—sterling appreciated and long-term interest rates fell below short rates for the first time in the decade. In the labor market, however, the response was perverse—the credibility of the policy was undermined by the substantial increase in public sector pay, the price effects of the near doubling of the value-added tax, and higher oil prices. Average earnings in manufacturing rose at an annual rate of 15.5 percent—or 2.5 percent in real terms—between 1978 and 1981, despite low productivity growth and rising unemployment. The coincidence of higher labor costs and a stronger exchange rate led to a real appreciation of sterling of about 60 percent between 1978 and the peak in the first part of 1981. This produced a rapid erosion of profitability and a substantial worsening of the competitive position of U.K. manufacturing.

The third phase, which began in 1981, is still too recent to be assessed fully. Preliminary evidence suggests that the anti-inflationary policy of the authorities has now won credibility in the labor market (albeit at a substantial cost), that a new realism in pay bargaining has emerged, and that there has been a substantial acceleration of productivity. The reduction in the wage gap, evident in the conventional measure, is obscured by the cyclical effect in the alternative measure. Purged of the cyclical effect, the alternative measure shows a fall in the gap of ½ of 1 percent in 1982. This implies that, although there has been some wage restraint, it has not been adequate to absorb the labor force.

III. Some Tentative Conclusions

The analysis in the paper leads to some tentative conclusions.

(1) As may be expected, the influence of prices of raw materials on manufacturing output and employment became sharply negative for both countries in the second decade (1973–82) of the sample period. In the first decade (1963–72), raw material cost developments had exerted a mildly positive influence, on average, in the United Kingdom and a slightly negative influence in Japan. A more interesting distinction between the countries relates to the effects of wage developments and the cyclical positions. In Japan in 1963–72, cyclical influences were, on average, positive with respect to output and employment, while labor cost developments had a strong negative effect. In 1973–82, cyclical influences became negative, and labor cost developments had a positive influence. In the United Kingdom, however, both cyclical and labor cost developments worsened from the first to the second decade of the sample period.

(2) An answer to the puzzle of the enormous wage gap in Japan, which emerges from the conventional analysis of the high-growth period 1966–72, is suggested by either the simulation exercise or the model-based wage gap calculations. This wage expansion appears to have been necessary to balance the rapidly growing demand for labor against the much slower labor force growth. Whereas wage movements in Japan usually appear to have been responsive to market forces, in the United Kingdom large wage increases appear to have occurred often despite considerable excess supply in the labor market.

(3) During the last few years of the sample period, excessive real wage growth has been much more of a problem for output, employment, and profit shares in the United Kingdom than in Japan. Recent history underscores the generalization that emerges from the entire sample period: in Japan increases in the share of labor in value added have tended to occur during periods of expansion and binding labor supply constraints; in the United Kingdom sharp increases in the share of labor costs have generally been correlated with recession and a fall in the demand for labor.

Four implications for macroeconomic policy emerge from a comparison of the data analyzed and the simple model illustrated in Figure 1.¹⁵

First, in both countries the weak cyclical position indicates that short-run gains in output and employment may be obtained by expansionary demand management. Present labor market conditions, however, suggest that these gains would be smaller in the United Kingdom than in Japan.

Second, the sustainability of any such gains would depend on whether an expansion of demand would elicit higher real wage demands. A priori one might expect this danger to be greater in Japan, where there is relatively less slack in the labor market, but the history of wage developments in the United Kingdom is less than comforting on this question. Another important factor is the response of capital investment to an expansion of demand. The relatively more favorable evolution of the share of capital in value added in Japan during recent years may mean that Japanese manufacturers are better placed to invest as a cyclical upturn occurs.

Third, in view of the size of the wage gap in both countries, policies to reduce the overhead costs of employment (such as the employers’ national insurance surcharge in the United Kingdom) are sensible; however, since unemployment is less of a problem and labor hoarding more of a problem in Japan than in the United Kingdom, the argument for such policies is stronger for the United Kingdom.

Finally, the analysis underscores the critical importance of one of the most fundamental policy initiatives of the present U.K. Government—that of altering the nature of wage bargaining to make it more responsive to market forces. To the extent that changes in labor legislation and bargaining practices achieve this end, a different pattern of comparative data might be forthcoming over the next decade.

APPENDICES

I. Data Sources

Japan

1. U.S. Department of Labor, Bureau of Labor Statistics, International Comparisons of Manufacturing Productivity and Labor Cost Trends (Washington: Government Printing Office, May 23, 1983).

Total hours worked in manufacturing (N) and total hourly compensation for employees (W) were taken from this source. The hourly compensation series includes workers’ earnings plus social security contributions paid by employers.

2. Japan, Economic Planning Agency, Stock of Capital in Private Enterprises (Tokyo: The Agency, various issues; in Japanese).

The gross capital stock of private manufacturers (excluding work in progress) in 1975 prices (K) and gross fixed investment by private manufacturers in 1975 prices (also excluding work in progress) were taken from this source.

3. Bank of Japan, Price Indexes Annual (various issues) and Economic Statistics Annual (Tokyo: Bank of Japan, various issues).

From these sources were taken the price index of manufactured output (P), the price index of raw materials inputs (PRM), manufactured output (Q), consumer prices, and the long-term interest rate. The output price index is the index for prices of manufactured goods taken from the wholesale price index (WPI). While the WPI coverage and weights differ from those that are appropriate for an output price index, the WPI series for output prices was compared with an index of manufactured output prices (available only since 1967) and found to be very similar. The price index for raw materials is the WPI for raw materials, taken from the WPI by special use.

4. Japan, Economic Planning Agency, Annual Report on National Income Accounts (Tokyo: The Agency, various issues; in Japanese).

Gross national expenditure, used to calculate the cyclical indicator (cyc), and shares of labor and capital in value added were taken from this source. The share of capital is calculated as

\frac{OS + DEP}{GO - IIM - IBT}

where

OS = operating surplus
DEP = depreciation
GO = gross output in the manufacturing sector
IIM = intermediate inputs
IBT = indirect business taxes less subsidies.

The share of labor is simply the ratio of total labor compensation (including social security contributions by employers) to gross output, less intermediate inputs and indirect business taxes less subsidies.

5. International Monetary Fund (unpublished data, Research Department).

Data on productivity, normalized to remove cyclical influences (as calculated in Artus (1977)), were obtained on request.

United Kingdom

1. United Kingdom, Statistical Service, Central Statistical Office, Economic Trends (London: Her Majesty’s Stationery Office, various monthly issues and annual supplement for 1983).

The series from this source were manufacturing output (Q), gross fixed investment in manufacturing, the output price index (P), the raw materials and fuels input price index for manufacturers (PRM), gross domestic product expenditure estimate in constant market prices (from which the cyclical indicator (cyc) was calculated), and total labor force. It is worth noting that the index of manufacturing output and the price index of manufacturing output are based on gross output—that is, they do not net out that part of manufacturing output that goes back into the manufacturing sector as an input. The implicit assumption here is that the share of gross manufacturing output that goes back into manufacturing is more or less constant over time in both value and volume.

2. United Kingdom, Central Statistical Office, National Income and Expenditure of the United Kingdom (London: Her Majesty’s Stationery Office, various issues).

The shares of labor and capital in value added in manufacturing were obtained from this source.

3. United Kingdom, Central Statistical Office, Input-Output Tables for the United Kingdom (1974), Business Monitor Series (London: Her Majesty’s Stationery Office, 1974).

This source was used to check the estimated value of the share of raw materials in total factor costs, β (see footnote 10). In the calculation, the numerator was total purchases of fuels and raw materials by manufacturing industry from both domestic and foreign sources. The denominator was gross output of manufacturing industry, less those intermediate inputs purchased from other domestic manufacturers. It is worth noting that only three factors of production are admitted: labor, capital, and raw materials. Inputs from other sectors (such as services) are aggregated with labor and capital, thereby raising the estimate of value added as a proportion of gross output. This presents less of a problem to the extent that labor and capital are the principal inputs in these other sectors, and prices of labor and capital are arbitraged between sectors.

4. U.S. Department of Labor, Bureau of Labor Statistics, International Comparisons of Manufacturing Productivity and Labor Cost Trends (Washington: Government Printing Office, May 26, 1983).

Total hours worked in the manufacturing sector (N) as well as nominal hourly earnings (W) were taken from this source. Hourly earnings are calculated from the perspective of costs to employers; as such they contain the employers’ national insurance contributions for employees as well as national insurance surcharges.

5. Bank of England (unpublished data, Economics Division).

Data on the cost of capital and the pretax real rate of return on capital were supplied by the Bank of England on request. However, these data are revised, updated, and published each year in the June issue of the Bank of England Quarterly Bulletin. For a description of the methodology employed in their derivation, see the March 1976 and June 1976 issues (Vol. 16, Nos. 1 and 2).

6. International Monetary Fund (unpublished data, Research Department).

Data on productivity, normalized to remove cyclical influences, and on the capital stock in manufacturing were obtained on request. Both series are based on calculations in Artus (1977).

II. Derivation of Equations for Estimated Output and Labor Demand

The Labor Demand Function¹⁶

The equation is based on a two-tier constant elasticity of substitution (CES) production function:

\begin{matrix} V^{ρ_{1}} = a {[N \cdot \exp (λ_{t} t - λ_{t} t^{2})]}^{ρ_{1}} + (1 - a) K^{ρ_{1}} & (7) \end{matrix}

\begin{matrix} Q^{ρ_{2}} = b V^{ρ_{2}} + (1 - b) R M^{ρ_{2}} . & (8) \end{matrix}

Equation (7) describes value added (V) as a function of labor (N) and capital (K) inputs, with technical progress characterized as a quadratic in time. The symbol “exp( )” denotes the exponent of the term in parentheses. Equation (8) describes gross output (Q) as a function of value added and raw material (RM) inputs. Both equations are restricted to exhibiting constant returns to scale:

ρ_{1} = (σ_{1} - 1) / σ_{1}

and

ρ_{2} = (σ_{2} - 1) / σ_{2}

where σ₁ is the elasticity of substitution between labor and capital and σ₂ is the elasticity of substitution between value added and raw materials.¹⁷

Taking first differences of natural logarithms of the first-order conditions of equation (7), ignoring technical progress for the moment, gives the following marginal product conditions:

\begin{matrix} - \frac{1}{σ_{2}} (\dot{v} - \dot{q}) - \frac{1}{σ_{1}} (\dot{n} - \dot{v}) = {\dot{w}}_{p} & (9) \end{matrix}

\begin{matrix} - \frac{1}{σ_{2}} (\dot{v} - \dot{q}) - \frac{1}{σ_{1}} (\dot{k} - \dot{v}) = {\dot{r}}_{p} & (10) \end{matrix}

where lowercase letters of variables (except for t) denote logarithms; dots represent first differences; and w_p is the wage rate and r_p the capital cost, both in terms of product prices. Substituting equation (10) into equation (9) yields

\begin{matrix} \dot{n} - \dot{k} = - σ_{1} {\dot{w}}_{p} + σ_{1} {\dot{r}}_{p} . & (11) \end{matrix}

Given homogeneity of degree one, from the dual of the production function, it is known that

\begin{matrix} {\dot{r}}_{p} = - (\frac{α}{γ}) {\dot{w}}_{p} - (\frac{β}{γ}) p \dot{r} m_{p} . & (12) \end{matrix}

where prm_p is the raw material price in terms of product price and α, γ, and β are, respectively, the cost shares of labor, capital, and raw materials in gross output.

The labor demand function is derived by substituting equation (12) into equation (11) and recalling, from the adding-up condition, that α + β + γ = 1, so that

\begin{matrix} \dot{n} - \dot{k} = - [σ_{1} (1 - β) / γ] {\dot{w}}_{p} - σ_{1} (\frac{β}{γ}) p \dot{r} m_{p} . & (13) \end{matrix}

It is estimated in level form, with a constant and with the technical progress terms reinserted.

Output

From equations (7) and (8), the partial derivative of gross output with respect to the labor input is

\begin{matrix} \frac{\partial Q}{\partial N} = ab N^{- 1 / σ_{1}} V^{(1 / σ_{1} - 1 / σ_{2})} Q^{1 / σ_{2}} & (14) \end{matrix}

which may be set equal to W_p as a first-order condition. In first differences of logarithms, this may be written as

\begin{matrix} σ_{2} {\dot{w}}_{p} = \dot{q} - (1 - \frac{σ_{2}}{σ_{1}}) \dot{v} - (\frac{σ_{2}}{σ_{1}}) \dot{n} . & (15) \end{matrix}

Given constant returns to scale, factor shares sum to unity, and therefore

\begin{matrix} Q = W_{p} N + R_{p} K + PR M_{p} RM . & (16) \end{matrix}

With fixed factor shares, this adding-up condition may be rewritten as

\begin{matrix} \dot{q} - \dot{k} = α (\dot{n} - \dot{k}) + β (\dot{r} m - \dot{k}) & (17) \end{matrix}

and

\begin{matrix} \dot{v} - \dot{k} = (\frac{α}{1 - β}) (\dot{n} - \dot{k}) . & (18) \end{matrix}

Substituting equation (18) into equation (15) and rearranging yields

\begin{matrix} \dot{n} = - (\frac{σ_{2}}{η}) {\dot{w}}_{p} + (\frac{1}{η}) \dot{q} + (\frac{η - 1}{η}) \dot{k} & (19) \end{matrix}

where

\begin{matrix} η = [{(1 - β)}^{- 1} {α + (\frac{σ_{2}}{σ_{1}}) (1 - α - β)}] . \end{matrix}

Substituting equation (19) into equation (17), and setting $\dot{r} m = \dot{q} - σ_{2} p \dot{r} m_{p}$ from the first-order conditions, yields

\begin{matrix} \dot{q} - \dot{k} = - (\frac{α σ_{1}}{γ}) {\dot{w}}_{p} - (\frac{βη σ_{1}}{γ}) p \dot{r} m_{p} . & (20) \end{matrix}

Clearly, unless σ₁ and σ₂ are valued at unity, factor shares are not constant over the sample period. For estimation, therefore, a linear approximation of both the labor demand and the output equation is employed around fixed factor shares that can be considered means. This involves simple estimation of the equations in level form and addition of an intercept term.¹⁸ In addition, a quadratic in time (t) is added to capture labor-saving technological change. Finally, these equations represent desired levels of output and employment on the basis of lagged, or correctly anticipated, relative prices and a given capital stock. Any deviation of actual (q and n) from desired (q* and n*) levels is due to cyclical factors that push producers off their normal output supply and labor demand curves. This may be characterized as

Q / Q^{*} = CY C^{m_{1}}

and

N / N^{*} = CY C^{m_{2}} .

In terms of logarithms, this requires that the term m₁cyc be added to the output equation and that m₂cyc be added to the labor demand equation. In both cases, lagged cyclical indicators were used. The equations for estimation, therefore, were as follows:

\begin{matrix} q - k & = - (α σ_{1} / γ) (w_{p} - λ_{1} t + λ_{2} t^{2}) \\ - [{β (σ_{1} α + σ_{2} γ)} / {(1 - β) γ}] pr m_{p} \\ + m_{1} cyc (- 1) + c_{1} & (21) \end{matrix}

\begin{matrix} n - k & = - [(1 - β) σ_{1} / γ] (w_{p} - λ_{1} t + λ_{1} t^{2}) - (β σ_{1} / γ) pr m_{p} \\ - λ_{1} t + λ_{1} t^{2} + m_{2} cyc (- 1) + c_{2} . & (22) \end{matrix}

Adjusting the Share of Raw Materials (β) for the Elasticity of Substitution

In calculating the “warranted” rate of real wage expansion, the relative price of capital and labor is held constant, thus eliminating any incentive for substitution between these factors. The price of raw materials, however, is allowed to vary, so that unless σ₂ is valued at unity factor shares will change. In calculating the warranted wage rate, this is taken into consideration in the following way. From equation (8) the first-order condition with respect to RM is

\frac{\partial Q}{\partial RM} = (1 - b) {(\frac{RM}{Q})}^{- 1 / σ_{2}} = PR M_{p}

therefore,

\begin{matrix} β = PR M_{p} (\frac{RM}{Q}) = {(1 - b)}^{σ_{2}} PR M^{1 - σ_{2}} & (23) \end{matrix}

and

\begin{matrix} \ln (β) = σ_{2} \ln (1 - b) + (1 - σ_{2}) pr m_{p} . & (24) \end{matrix}

It is easy to get an estimate of (1 − b) from the estimates of σ₂, the mean value of prm_p, and the estimate (that is, the mean sample value) of β. Thus,

\begin{matrix} \ln (\hat{1 - b}) = \frac{1}{σ_{2}} \ln (\hat{β}) - (\frac{\hat{1 - σ_{2}}}{σ_{2}}) \bar{pr m_{p}} & (25) \end{matrix}

where the circumflex (ˆ) indicates estimated value and the bar (¯) indicates mean value. It is then possible to derive a series for β that takes into account relative price movements and the elasticity of substitution, so that

\begin{matrix} \ln (β) = σ_{2} \ln (\hat{1 - b}) + (\hat{1 - σ_{2}}) pr m_{p} . & (26) \end{matrix}

REFERENCES

Artus, Jacques A., “Measures of Potential Output in Manufacturing for Eight Industrial Countries, 1955–78,” Staff Papers, International Monetary Fund (Washington), Vol. 24 (March 1977), pp. 1–35.
- Search Google Scholar
- Export Citation
Artus, Jacques A., “The Disequilibrium Real Wage Rate Hypothesis: An Empirical Evaluation,” Staff Papers, International Monetary Fund (Washington), Vol. 31 (June 1984), pp. 249–302.
- Search Google Scholar
- Export Citation
Basevi, Giorgio, and others, Macroeconomic Prospects and Policies for the European Community, Economic Papers, No. 12 (Brussels: Commission of the European Communities, Directorate-General for Economic and Financial Affairs, April 1983).
- Search Google Scholar
- Export Citation
Berndt, Ernst R., and David O. Wood, “Engineering and Econometric Interpretations of Energy-Capital Complementarity,” American Economic Review (Nashville, Tennessee), Vol. 69 (June 1979), pp. 342–54.
- Search Google Scholar
- Export Citation
Bruno, Michael, Raw Materials, Profits, and the Productivity Slowdown, Working Paper No. 660 (Cambridge, Massachusetts: National Bureau of Economic Research, April 1981).
- Search Google Scholar
- Export Citation
Bruno, Michael, and Jeffrey Sachs, Macroeconomic Adjustment with Import Price Shocks: Real and Monetary Aspects, Working Paper No. 340 (Cambridge, Massachusetts: National Bureau of Economic Research, April 1979).
- Search Google Scholar
- Export Citation
Bruno, Michael, and Jeffrey Sachs, “Input Price Shocks and the Slowdown in Economic Growth: The Case of U.K. Manufacturing,” Review of Economic Studies (Clevedon, England), Vol. 49, Special Issue (No. 159, 1982), pp. 679–705.
- Search Google Scholar
- Export Citation
Buiter, Willem H., and Marcus Miller, “The Thatcher Experiment: The First Two Years,” Brookings Papers on Economic Activity: 2 (1981), The Brookings Institution (Washington), pp. 315–79.
- Search Google Scholar
- Export Citation
Buiter, Willem H., and Marcus Miller, “Changing the Rules: Economic Consequences of the Thatcher Regime,” Brookings Papers on Economic Activity: 2 (1983), The Brookings Institution (Washington), pp. 305–79.
- Search Google Scholar
- Export Citation
Dunlop, John T., “The Movement of Real and Money Wage Rates,” Economic Journal (Cambridge, England), Vol. 48 (September 1938), pp. 413–34.
- Search Google Scholar
- Export Citation
Grubb, D., R. Jackman, and R. Layard, “Causes of the Current Stagflation,” Review of Economic Studies (Clevedon, England), Vol. 49, Special Issue (No. 159, 1982), pp. 707–30.
- Search Google Scholar
- Export Citation
Keynes, John Maynard, The General Theory of Employment, Interest, and Money (New York: Harcourt, Brace & World, 1936).
- Search Google Scholar
- Export Citation
Lipton, D.A., Accumulation and Growth in Open Economies” (doctoral dissertation, Cambridge, Massachusetts: Harvard University, 1979).
- Search Google Scholar
- Export Citation
Malinvaud, Edmond, The Theory of Unemployment Reconsidered” (New York: John Wiley, 1977).
- Search Google Scholar
- Export Citation
Mundell, Robert A., “An Exposition of Some Subtleties in the Keynesian System,” Weltwirtschaftliches Archiv (Kiel), Vol. 93 (No. 2, 1964), pp. 301–13.
- Search Google Scholar
- Export Citation
Otani, Ichiro, “Real Wages and Business Cycles Revisited,” Review of Economics and Statistics (Amsterdam), Vol. 60 (May 1978), pp. 301–04.
- Search Google Scholar
- Export Citation
Sachs, Jeffrey D., “Wages, Profits, and Macroeconomic Adjustment: A Comparative Study,” Brookings Papers on Economic Activity: 2 (1979), The Brookings Institution (Washington), pp. 269–320.
- Search Google Scholar
- Export Citation
Sachs, Jeffrey D., “Real Wages and Unemployment in the OECD Countries,” Brookings Papers on Economic Activity: 1 (1983), The Brookings Institution (Washington), pp. 255–89.
- Search Google Scholar
- Export Citation
Tarshis, Lorie, “Notes and Memoranda: Changes in Real and Money Wages,” Economic Journal (Cambridge, England), Vol. 49 (March 1939), pp. 150–54.
- Search Google Scholar
- Export Citation

Mr. Lipschitz, a senior economist in the European Department, holds degrees from the London School of Economics and Political Science and the University of London. This paper was written while he was on leave from the Fund as a guest scholar at the Brookings Institution.

Ms. Schadler, a senior economist in the Asian Department, holds degrees from Mount Holyoke College and the London School of Economics and Political Science.

The authors wish to acknowledge comments on the paper by colleagues in the Fund and by Harold Furchgott-Roth, Kazumasa Iwata, Robert Lawrence, Yuzuru Ozeki, Yoichi Takahashi, and Heizo Takenaka.

Enormous debts to work done outside the Fund will also be apparent to the informed reader. In particular, papers by Sachs (1979), Bruno (1981), Bruno and Sachs (1979 and 1982), Grubb, Jackman, and Layard (1982), and Basevi and others (1983) have been extremely helpful.

Throughout this paper, real wages and real prices of raw materials refer to nominal wages and raw material prices that are deflated by the price of manufactured output. These terms should be distinguished from nominal wages or materials prices that are deflated by consumer prices. The latter are relevant to wage earners or consumers, the former to producers.

If output prices responded to demand while nominal wages were relatively sticky, a further demand expansion might indeed be effective in reducing real wages. Insofar as workers are in a position to restore the real wage level to W₀, however, the gain will be only transitory. The characterization of the “Keynesian” view in this section refers to modern Keynesians rather than to Keynes himself. The classical view that real wages are countercyclical was actually retained by Keynes (see The General Theory (1936), Chapter 20), but has since been the subject of great debate; see, for example, Dunlop (1938), Tarshis (1939), and Malinvaud (1977). Otani (1978) provides a useful examination of the recent data, and Sachs (1983) has an excellent discussion of this point.

For the purpose of this exercise, labor and raw materials are assumed to be variable inputs, whereas the capital stock is assumed to be fixed in the short run. Despite lifetime employment practices affecting many workers in Japan’s manufacturing sector, labor can be viewed as a variable input because of the substantial variations in average working hours and the flexibility with which a large number of young women enter and leave the work force.

The equilibrium version of equations (1) and (2)—when cyclical influences are neutral—is derived from a two-tier, constant elasticity of substitution (CES) production function, which is one of the simplest ways to characterize the case of three factors of production. This involves the specification of gross output as a function of value added and raw material inputs, and of value added as a function of labor and capital:

\begin{matrix} V^{ρ_{1}} = a {[N \cdot \exp (λ_{1} t - λ_{1} t^{2})]}^{ρ_{1}} + (1 - a) K^{ρ_{1}} & (valueadded) \end{matrix}

\begin{matrix} Q^{ρ_{2}} = b V^{ρ_{2}} + (1 - b) R M^{ρ_{2}} & (grossoutput) \end{matrix}

where ρ₁ = (σ₁ − 1)/σ₁ and ρ₂ = (σ₂ − 2)/σ₂, and σ₁, σ₂, are elasticities of substitution between labor and capital, and between value added and raw materials, respectively. V is value added, RM the raw materials input, and N the labor input. Several simplifications implicit in this model should be noted: (1) the aggregation of energy and other raw material inputs ignores possible differences between the effects of changes in their prices; (2) all technological progress is labor saving; and (3) the degree to which technology is capital intensive (as indicated by a) and raw material intensive (as indicated by b) is fixed over the time period. For an examination of bias resulting from some of these simplifications, see Artus (1984; this issue). Appendix II provides a detailed derivation of equations (1) and (2) from profit maximization, subject to these production functions.

For Japan, gross national expenditure was used; for the United Kingdom, gross domestic expenditure was used. The t² is included to capture the slowdown in growth during the sample period.

The mean of the ratio of the value of labor to capital inputs (α/γ), which is available from national accounts statistics, was imposed in the estimation to improve the efficiency of results.

The coefficient on t² was not significantly different from zero in preliminary estimation results for Japan and was dropped from the final estimation.

For example, a zero elasticity of substitution implies that the given technology allows no substitution to occur. An increase in the relative price of raw materials simply leads to a corresponding increase in the share of raw materials in total costs, which must be offset by a lower share for labor and for capital. An elasticity of substitution equal to unity implies that a given increase in the relative price of raw materials would lead to a proportionately equal decline in the volume of raw material inputs so that the shares of labor, capital, and raw materials in total costs would remain constant.

Gross output is defined as output of manufacturing industries, less the part of output that serves as an intermediate input into other manufacturing industries. Raw material and fuel inputs in 1974 constituted 17.8 percent of gross output. The estimated share (β), adjusted for relative price changes given the estimated elasticity of substitution, amounted to 16.8 percent in 1974 and 18.3 percent in 1975. This is remarkably close to the input-output coefficient.

This is oversimplified, insofar as only three factors are admitted. In fact, the share of value added is somewhat lower when inputs of other sectors—such as services, construction, and the like—are allowed. It is implicitly assumed that the prices of labor and capital move similarly in these sectors and that the share of raw materials in these sectors is negligible.

For each country, the wage gap index is simply an index of the actual over the warranted real wage level.

The size of the wage gap is, of course, extremely sensitive to the assumption about the labor supply. The methodology employed by Artus (1984) implicitly incorporates the effects of structural change in the estimates of the labor supply. This is not particularly important for Japan, for which—despite the differences in methodology—the two studies find almost identical absolute increases in the wage gap over the period 1963–82 (although the timing of the movements in the wage gap differs for reasons detailed in Artus’s study). For the United Kingdom, however, by incorporating the calculated effects of structural change on the labor supply available to manufacturing, Artus finds a much smaller wage gap than is found in the present study. Indeed, according to his results, the absolute increase in the wage gap for the United Kingdom during 1963–82 is about the same size as that for Japan.

The rate of change in real terms fell from −1 percent a year in 1973–75 to −5 percent a year in 1976–77.

It should be clear that the partial equilibrium nature of the estimated model prevents a firm conclusion on the sustainability of gains from more expansionary demand management policies. The analysis in this paper is designed, rather, to assess the relative cost position of manufacturers as one factor that could limit the effectiveness of such policies for countercyclical purposes.

The derivations presented in this appendix draw heavily on Bruno and Sachs (1979 and 1982).

The use of two-tier production functions does have certain restrictive implications for substitution among the three factors of production. For example, the separability of raw materials implicit in the two-tier production functions ensures that an increase in the price of raw materials reduces the demand for labor. If the three factors of production were included in a single production function, this would not necessarily be the case. Various empirical studies of the United States and Japan, however, suggest that the restrictive form of the production function is not inconsistent with the data. See Berndt and Wood (1979) and Lipton (1979).

For similar treatment, see Bruno and Sachs (1982). As they point out, an equation $\dot{z} = a \dot{x} + b \dot{y}$ can be transformed to z = c + ax + by, where $\dot{x} = x - \bar{x}$ and $c = \bar{z} - a \bar{x} - b \bar{y}$ .

Other Publishers

Save
Cite
Email this content

Share Link

Copy this link, or click below to email it to a friend
Email this content
or copy the link directly:

https://www.elibrary.imf.org/view/journals/024/1984/002/article-A002-en.xml
The link was not copied. Your current browser may not support copying via this button.

Link copied successfully

Collapse
Expand

IMF Staff papers: Volume 31 No. 2

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1984: Issue 002

Publisher:: International Monetary Fund

ISBN:: 9781451946918

ISSN:: 1020-7635

Pages:: 198

DOI:: https://doi.org/10.5089/9781451946918.024

Keywords
APPENDICES
- I. Data Sources
- II. Derivation of Equations for Estimated Output and Labor Demand
REFERENCES

View raw image

Chart 1.

Japan and the United Kingdom: Performance in the Manufacturing Sector, 1963–82

(Annual percentage change)

View raw image

Figure 1.

Keynesian and Classical Unemployment

View raw image

Chart 2.

Japan: Actual and Warranted Real Wage Developments, 1962–82

View raw image

Chart 3.

United Kingdom: Actual and Warranted Real Wage Developments, 1962–82

View raw image

Chart 4.

Japan and the United Kingdom: Wage Gap Indices,¹ 1963–82

View raw image

Chart 5.

Japan and the United Kingdom: Labor Demand in Manufacturing and Total Labor Force Growth,¹ 1963–82

View raw image

Chart 6.

Japan and the United Kingdom: Alternative Wage Gap Indices,¹ 1963–82

Table 5.

Japan and the United Kingdom: Components of Change in Output and Labor Demand, 1963–82

(Annual percentage change)

			1963–72		1973–82
Item			Japan	United Kingdom	Japan	United Kingdom
Output			11.561	3.037	3.222	−1.235
	Wages¹		−2.855	−0.987	0.680	−1.620
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.346	0.194	−2.653	−1.288
	Cyclical influence		1.404	0.084	−1.069	−0.386
	Unexplained residual		0.473	−0.429	−0.071	0.045
Labor demand			1.611	−1.540	−0.288	−3.910
	Wages¹		−5.640	−1.387	1.344	−2.276
	Capital		12.885	4.175	6.335	2.014
	Materials prices		−0.285	0.192	2.187	−1.272
	Cyclical influence		0.279	0.105	−0.213	−0.483
	Labor-saving
		technology	−5.635	−3.943	−5.635	−1.708
	Unexplained residual		−0.007	−0.682	−0.358	−0.185

^¹Adjusted for changes in productivity.

Topics

Countries

Series

About

Resources

Abstract

I. Relative Prices and Cyclical Influences in the Manufacturing Sector

two views

the model

II. Wage Push, Factor Shares, and Employment

actual and warranted wage increases: the conventional analysis

the supply of labor and the real wage

an alternative warranted wage calculation

III. Some Tentative Conclusions

APPENDICES

I. Data Sources

Japan

United Kingdom

II. Derivation of Equations for Estimated Output and Labor Demand

The Labor Demand Function16

Output

Adjusting the Share of Raw Materials (β) for the Elasticity of Substitution

REFERENCES

Same Series

Other IMF Content

Other Publishers

Asian Development Bank

Inter-American Development Bank

The World Bank

Share Link

Table of Contents

Headings

Figures

Metrics

The Labor Demand Function¹⁶